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TP A2 UP I: Ferromagnetic Resonance (FMR)
(K.
Lenz, J. Lindner, E. Kosubek, K. Baberschke)
FMR is one of the best techniques to determine
the intrinsic magnetic anisotropy energy (MAE) quantitatively
and with high precision. The temperature, angular and frequency dependent
measurements in situ in UHV yield second- and fourth-order,
in-plane and out-of-plane MAE constants as a function of temperature.
All MAE constants are separated into interface and volume contributions
K i = Ki V
+2Ki S/d
by investigations at different film thickness d and at constant reduced
temperature t = T/TC(d). Simultaneously the anisotropy of
the orbital magnetic moment can be determined by the spectroscopic
splitting factor, i. e. the g-tensor from the simple relation µL/µS
= (g-2)/2 [Ref. 171, 210] . These experiments
help to understand how these quantities are modified in 3d and
4f films and sandwiches relative to the bulk. Extrapolation of the
measured MAE constants to T=0K yields a direct comparison to first principles
MAE calculations. In addition the magnetization dynamics and spin fluctuations
on the nanosecond scale can be studied and the temperature dependence
of the total magnetization of monolayers can be determined. Some highlights
are given below.
Both regions are separated by the green shaded space in which an equilibrium tilted magnetization is measured. Using the yellow lines as a guide one observes an anomalous reorientation from in-plane to out-of-plane with increasing thickness or temperature . This is opposite to the conventional observation in Fe and Co layers. The magnetization rotates as a function of temperature (fixed d) as well as a function of thickness (fixed T) continuously, indicating a second order transition.
This unconventional reorientation is quantitatively understood by
the measured temperature dependencies of interface and volume MAE
[Ref.
180,185] as shown in Fig. 2. K2V
is positive favoring a perpendicular orientation while K2 S is negative favoring an in-plane magnetization.
Both decrease as a function of temperature. The different temperature
dependencies and the thickness dependent balance of shape anisotropy and
intrinsic MAE explain the magnetic phase diagram of Fig.1 quantitatively.
Fourth-order anisotropy constant must be included in the free energy
density E to explain the tilted orientation (green area) in Fig.1
. In Fig. 3 (on the left) we show the threedimensional parameter set
K 4|| = f(K2) and K4perp = f(K2).
All Ki are normalized to 2piM2 [Ref. 176, 184]
. The light blue (yellow) areas indicate an easy in-plane
(perpendicular) spontaneous magnetization. The white region presents
the parameter space for a tilted orientation. The MAE constants
vary as a function of film thickness and temperature. For different
samples, temperatures and thicknesses the experimental data are indicated.
As an example we show values for Ni/Cu(001) near the reorientation
(green area in Fig.1) and for Ni(111)/W(110) [Ref. 120, 171] .
Ni/W has very small K4 and K2 values (open squares),
consequently this film has its easy axis in-plane under all conditions.
Contrary Ni/Cu with large uniaxial K2 values and moderate (negative
and positive) K4 values permits all orientations as an easy
axis. The physical reason for this is the pseudomorphic growth and its
tetragonal distortion, whereas Ni/W grows in an undistorted cubic phase.
Recently
we have employed FMR to measure the magnetic anisotropy constants
and the spectroscopic g tensor of high quality single-crystalline
Fe/V superlattices (SL) on MgO(001). The samples were provided from
the Group of R. Waeppling, Uppsala
University . FMR is the most suitable technique for determining
all magnetic anisotropy constants via angular-dependent measurements
[e.g. Refs. 184,193,235]. In Fig. 4 we show full polar- and azimuthal-angular-dependent
FMR measurements of the resonance field Hr for an (Fe4/V4
)40 SL on MgO(001). The indices 4 are MLs of Fe or V
in one period, while 40 is the number of SL periods. From the positions
of the Hr -minima at qH=
±90o , Fig. 4(a), we conclude that the magnetization
lies in the film plane. In Fig. 4(b) we see a small in-plane anisotropy
with minima along the [100] and [010] directions. In addition a smaller
asymmetry between the two ideally identical [100] and [010] directions
indicates the presence of a small step-induced anisotropy [Ref. 193] .
Frequency-dependent FMR measurements probe the components of the g
tensor and through this the orbital magnetism through the equation:
µL/µS =
(g-2)/2
[Refs. 210, 234, 271] . FMR is the only technique that may provide
independently values for the MAE and the anisotropy of the orbital
moment (through measurements of the components of the g tensor). In
Fig. 5(a) (on the left) we present the components g// of
the g tensor in the film plane for two Fe/V superlattices. The values
of g// are larger than the values of bulk Fe. Since g is
a function of the magnetic moment it is temperature-independent. Note
also that for the sample Fe2/V5 we probe g//
at temperatures higher than TC as the magnetic moment persists
above TC. Unlike g//, MAE is temperature-dependent.
This is demonstrated in Fig. 5(b) for both Fe/V samples. For the Fe
2/V5 sample we may see that MAE vanishes at TC
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